Bulk-boundary correspondence in Josephson Junctions

TL;DR

This paper explores the bulk-boundary correspondence in Josephson junctions between topological superconductors, revealing that zero-energy bound states depend on differences in topological invariants like winding and Chern numbers.

Contribution

It generalizes the bulk-boundary correspondence concept to Josephson junctions involving topological superconductors, linking bound states to topological number differences.

Findings

Zero-energy bound states appear when topological numbers differ.

Number of bound states equals the absolute difference of topological invariants.

Bound states are independent of junction parameters such as phase difference.

Abstract

We discuss bound states appearing at the interface between two different superconductors characterized by different nontrivial topological numbers such as one-dimensional winding numbers and Chern numbers. The one-dimensional winding number characterizes d_{xy} and p_x wave superconductors. The Chern number characterizes chiral-p, chiral-d, and chiral-f wave superconductors. The interfacial bound state appears at the zero-energy when the topological numbers of the two superconductors are different from each other. When the two superconductors are characterized by the Chern numbers n and m, for example, the number of the zero-energy bound is |n-m| independent of junction parameters such as the phase difference across the junction and the transmission probability of interface. We generalize a concept of bulk-boundary correspondence to the Josephson junctions consisting of two topological superconductors.